Ratio-dependent predator prey models are favored by many animal ecologists recently as more suitable ones for predator-prey interactions where predation involves searching process. In this paper, a ratio-dependent pre...Ratio-dependent predator prey models are favored by many animal ecologists recently as more suitable ones for predator-prey interactions where predation involves searching process. In this paper, a ratio-dependent predator prey model with stage structure and time delay for prey is proposed and analyzed. In this model, we only consider the stage structure of immature and mature prey species and not consider the stage structure of predator species. We assume that the predator only feed on the mature prey and the time for prey from birth to maturity represented by a constant time delay. At first, we investigate the permanence and existence of the proposed model and sufficient conditions are derived. Then the global stability of the nonnegative equilibria are derived. We also get the sufficient criteria for stability switch of the positive equilibrium. Finally, some numerical simulations are carried out for supporting the analytic results.展开更多
In this paper, we investigate the existence, stability and global attractivity of T-periodic solutions for a class of quasilinear parabolic equations under Robin boundary conditions. We obtain that periodic solutions ...In this paper, we investigate the existence, stability and global attractivity of T-periodic solutions for a class of quasilinear parabolic equations under Robin boundary conditions. We obtain that periodic solutions exist if the inter-specific competition rates are weak. The numerical simulations are also presented to illustrate our result.展开更多
文摘Ratio-dependent predator prey models are favored by many animal ecologists recently as more suitable ones for predator-prey interactions where predation involves searching process. In this paper, a ratio-dependent predator prey model with stage structure and time delay for prey is proposed and analyzed. In this model, we only consider the stage structure of immature and mature prey species and not consider the stage structure of predator species. We assume that the predator only feed on the mature prey and the time for prey from birth to maturity represented by a constant time delay. At first, we investigate the permanence and existence of the proposed model and sufficient conditions are derived. Then the global stability of the nonnegative equilibria are derived. We also get the sufficient criteria for stability switch of the positive equilibrium. Finally, some numerical simulations are carried out for supporting the analytic results.
文摘In this paper, we investigate the existence, stability and global attractivity of T-periodic solutions for a class of quasilinear parabolic equations under Robin boundary conditions. We obtain that periodic solutions exist if the inter-specific competition rates are weak. The numerical simulations are also presented to illustrate our result.
